Problem 5 (20 marks): A cost payoff table is given as Cost Payoff Table State of Nature Decision s1 s2 d1 358 757 d2 951 444 d3 332 377 s3 809 1035 763 a. What choice should be made by the optimistic decision maker? (3 mark) b. What choice should be made by the conservative decision maker? (3 mark) c. What decision should be made under minimax regret? (3 marks) d. If the P(s)=0.2, P(S2)=0.5, and P(53)=0.3, respectively, then what choice should be made under expected value? (2 marks) e. What is the EVPI? (3 marks) f. If the conditional probabilities obtained from sample information I are P(I | S)=0.1, P(I | s2)= 0.05, P(I | S3)= 0.2, compute the revised or posterior probabilities P(si (1), P(s2 | 1) and P(s3 | 1). (4 marks) g. Compute expected values for each decision using the revised probabilities, obtained from part f. What choice should be made? (2 marks) HINT: You must show all computations in detail